To make the butterscotch sauce, in a saucepan over medium heat, combine brown sugar, whole milk, butter, and vanilla extract. Use a whisk to combine, keep smooth, and cook until thickened. Allow the butterscotch sauce to cool before making the ice cream.
In a large bowl whisk together heavy cream, sweetened condensed milk, vanilla extract and cooled butterscotch sauce (except about a tablespoon which will top the ice cream). Once combined, turn on your ice cream maker and pour the ice cream mixture into it. Run the ice cream maker for 15-20 minutes.
Pour into your ice cream storage container, drizzle the remaining butterscotch sauce on top, and swirl it into the ice cream.
Serve or freeze for later. Ice cream will be very soft right out of the machine.
Tip: When making ice cream be sure to keep your cold ingredients in the fridge and your ice cream insert in the freezer until you are ready to use.